Subproject A7: Shaping the dynamics of interconnected cycles – optimal control using fuzzy logic based models

The subproject A7 is engaged in a mathematical modelling of interconnected cycles, and the thereby enabled system analysis. The use of a mathematical model grants access to a wide range of computer-assisted tools for analysis, control and optimisation of the cyclic system and its parameters. It is therefore the ambition of subproject A7 to develop and explore methods, regularly used in control theory, to control and shape the dynamics of interconnected cycles, as well as to provide tools for the analysis of system properties, like stability and robustness.

Motivation

Representation of interconnected cycles by a dynamical model through
- Expert knowledge: e.g. linguistic “if – then” rules
- Data of past cycles, e.g. sales figures
Analysis of system properties, like
- Stability of the system in given scenarios
- Robustness against perturbations
- Controllability and observability of the system states
Methodical shaping of system dynamics through appropriate control of system input
Recommendations for decision making by optimisation of different factors of interest

Results of funding period 2

System modelling using approaches from the field of computational intelligence, e.g. Takagi-Sugeno fuzzy models
Development of methods for the approximate the domain of stability and for feedback-control
- Optimal layout of control parameters through convex optimisation
- Development of system control methods under consideration of input constrains (e.g. maximal number of employees)
- Approximation of the domain of stability of the dynamical model using linear matrix inequalities
Validation of the methods on technical systems

Prospective results of funding period 3

Enhancement of the dynamical model and improvement of the approximation quality
- Allowance of statistical uncertainties in the model dynamics
- Modelling of delayed influences (dead time)
- Modelling of discrete events (e.g. new law coming into force)
Development of control methods for the established models
- Methods to shape the stability domain
- Observer and control concepts
Development of a guideline on the handling and control of the dynamics of interconnected cycles
- Development of a procedure model for the effective application of the evaluated methods

Selected publications

Diepold K.J.; Albert K.: Lokale Stabilitätsnalyse von Takagi-Sugeno Systemen unter Berücksichtigung ihres Gültigkeitsbereichs. In: at-Automatisierungstechnik 62 (2014) 10, S. 687-697
Kindsmüller T.M.; Behncke F.G.H.; Stahl B.; Diepold K.J.; Wickel M.C.; Kammerl D.; Kernschmidt K.: Mitigating the Effort for Engineering Changes in Product Development Using a Fuzzy Expert System. In: IEEE International Technology Management Conference, 2014, Chicago, S. 602-606
Stahl B.; Diepold K.J.: Pohl J.; Greitemann J.; Plehn C.; Koch J. Lohmann B.; Reinhart G..: Modeling Cyclic Interactions within a Production Environment using Transition Adaptive Recurrent Fuzzy Systems. In: IFAC Conference on Manufacturing Modelling, Management and Control, 2013, Sankt Petersburg, S. 1979-1984

Principal investigators

Prof. Dr.-Ing. Boris Lohmann
Subprojects A3 and A7
Chair of Automatic Control
lohmann@tum.de
Tel.: +49 (0) 89 289 15610

Researchers

Christian Dengler M. Sc.
Subproject A7
Chair of Automatic Control
c.dengler@tum.de
Tel.: +49 (0) 89 289 15664